An Introduction to Linear AlgebraClarendon Press, 1972 - 440 pages |
À l'intérieur du livre
Résultats 1-3 sur 87
Page 169
... suppose that ( 6.1.1 ) holds for every x € S and for every N = 0 ; in other words , suppose that ƒ is invariant under every operator of the set . If now the determination of ƒ ( x ) , for some particular xo e 6 , is difficult or tedious ...
... suppose that ( 6.1.1 ) holds for every x € S and for every N = 0 ; in other words , suppose that ƒ is invariant under every operator of the set . If now the determination of ƒ ( x ) , for some particular xo e 6 , is difficult or tedious ...
Page 218
... Suppose that all characteristic roots of I - A are less than 1 in modulus . Prove that 0 < | det A | < 2 ′′ ; and show that this result is best possible . 27. Let A = ( a ,, ) be a real n × n matrix and suppose that App > Σ | αrs ...
... Suppose that all characteristic roots of I - A are less than 1 in modulus . Prove that 0 < | det A | < 2 ′′ ; and show that this result is best possible . 27. Let A = ( a ,, ) be a real n × n matrix and suppose that App > Σ | αrs ...
Page 249
... suppose that | A | Show that A + B is singular . 17. Let x ) = -B . ( X ) be an orthogonal matrix and suppose that x # 0. Show :) that -1 < a < 1 , and prove that A + bxyT is orthogonal if and only if b = ( 1 - a ) -1 or b = − ( 1 + a ) ...
... suppose that | A | Show that A + B is singular . 17. Let x ) = -B . ( X ) be an orthogonal matrix and suppose that x # 0. Show :) that -1 < a < 1 , and prove that A + bxyT is orthogonal if and only if b = ( 1 - a ) -1 or b = − ( 1 + a ) ...
Table des matières
DETERMINANTS VECTORS MATRICES | 1 |
VECTOR SPACES AND LINEAR MANIFOLDS | 39 |
THE ALGEBRA OF MATRICES | 72 |
12 autres sections non affichées
Autres éditions - Tout afficher
Expressions et termes fréquents
A₁ algebra assertion automorphism B₁ basis bilinear form bilinear operator C₁ canonical forms characteristic roots characteristic vectors coefficients columns commute complex numbers convergent coordinates Deduce defined denote determinant diagonal form diagonal matrix E-operations equal equivalence EXERCISE exists follows functions given Hence hermitian form hermitian matrix identity implies inequality integers invariant space isomorphic linear equations linear manifold linear transformation linearly independent matrix group matrix of order minimum polynomial multiplication non-singular linear transformation non-singular matrix non-zero numbers nxn matrix obtain orthogonal matrix positive definite positive semi-definite possesses proof of Theorem prove quadratic form quadric rank relation represented respect result rotation S-¹AS satisfies scalar Show similar singular skew-symmetric matrix solution square matrix suppose symmetric matrix t₁ tion triangular unique unit element unitary matrix values vector space view of Theorem write x₁ xTAx y₁ zero α₁